Abstract

For an uncalibrated camera, the problem of automatically determining the correspondences of four given coplanar points has not yet been solved. Previous algorithms [mostly related to two-dimensional (2D) homography] avoided this correspondence problem and required people to manually choose the correct image point one by one. In this paper, we propose a novel three-step method to automatically identify the correct correspondence. First, prejudge the possibilities of correspondences (PoC) based on the analysis of why ambiguous correspondences occur. Second, set a cuboid bound for the optical center to verify if the center circle computed from the homography intersects it. Third, utilize the reasonability and stability of the intrinsic parameters to remove the still-wrong PoC. Besides applications in recovering 2D Euclidean structure and camera calibration, we can also extend the proposed method to detect multiple quadrangle objects, no matter if they are coplanar or not. Many experiments with simulated and real data show that our method has good performance and important applied value.

© 2012 Optical Society of America

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  1. C. Rothwell, A. Zisserman, C. Marinos, D. Forsyth, and J. Mundy, “Relative motion and pose from arbitrary plane curves,” Image Vis. Comput. 10, 250–262 (1992).
    [CrossRef]
  2. S. Ma, “Conics-based stereo, motion estimation, and pose determination,” Int. J. Comput. Vis. 10, 7–25 (1993).
    [CrossRef]
  3. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Patt. Anal. Mach. Intell. 22, 1330–1334 (2000).
    [CrossRef]
  4. P. Sturm and S. Maybank, “On plane-based camera calibration: a general algorithm, singularities, applications,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 432–437.
  5. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University, 2003).
  6. D. Liebowitz and A. Zisserman, “Metric rectification for perspective images of planes,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1998), pp. 482–488.
  7. J. Bouguet, Camera Calibration Toolbox for MATLAB, http://www.vision.caltech.edu/bouguetj/calib_doc/ .
  8. Y. Ma, S. Soatto, J. Koseck, and S. S. Sastry, An Invitation to 3-D Vision (Springer, 2003).
  9. M. A. Fischler and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM 24, 381–395 (1981).
    [CrossRef]
  10. M. Zuliani, C. S. Kenney, and B. S. Manjunath, “The multiRANSAC algorithm and its application to detect planar homographies,” in Proceedings of the International Conference on Image Processing (IEEE, 2005), pp. III, 153–156.
  11. https://github.com/RANSAC/RANSAC-Toolbox .
  12. P. Gurdjos, A. Crouzil, and R. Payrissat, “Another way of looking at plane-based calibration: the Centre Circle constraint,” in Proceedings of the European Conference on Computer Vision (Springer, 2002), pp. 252–266.
  13. J. V. Poncelet, Applications d’Analyse et de Geometrie—Traite des Proprietes Projectives des Figures, Tome I (Imprimerie de Mallet-Bachelier, 1862).

2000

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Patt. Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

1993

S. Ma, “Conics-based stereo, motion estimation, and pose determination,” Int. J. Comput. Vis. 10, 7–25 (1993).
[CrossRef]

1992

C. Rothwell, A. Zisserman, C. Marinos, D. Forsyth, and J. Mundy, “Relative motion and pose from arbitrary plane curves,” Image Vis. Comput. 10, 250–262 (1992).
[CrossRef]

1981

M. A. Fischler and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM 24, 381–395 (1981).
[CrossRef]

Bolles, R. C.

M. A. Fischler and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM 24, 381–395 (1981).
[CrossRef]

Crouzil, A.

P. Gurdjos, A. Crouzil, and R. Payrissat, “Another way of looking at plane-based calibration: the Centre Circle constraint,” in Proceedings of the European Conference on Computer Vision (Springer, 2002), pp. 252–266.

Fischler, M. A.

M. A. Fischler and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM 24, 381–395 (1981).
[CrossRef]

Forsyth, D.

C. Rothwell, A. Zisserman, C. Marinos, D. Forsyth, and J. Mundy, “Relative motion and pose from arbitrary plane curves,” Image Vis. Comput. 10, 250–262 (1992).
[CrossRef]

Gurdjos, P.

P. Gurdjos, A. Crouzil, and R. Payrissat, “Another way of looking at plane-based calibration: the Centre Circle constraint,” in Proceedings of the European Conference on Computer Vision (Springer, 2002), pp. 252–266.

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University, 2003).

Kenney, C. S.

M. Zuliani, C. S. Kenney, and B. S. Manjunath, “The multiRANSAC algorithm and its application to detect planar homographies,” in Proceedings of the International Conference on Image Processing (IEEE, 2005), pp. III, 153–156.

Koseck, J.

Y. Ma, S. Soatto, J. Koseck, and S. S. Sastry, An Invitation to 3-D Vision (Springer, 2003).

Liebowitz, D.

D. Liebowitz and A. Zisserman, “Metric rectification for perspective images of planes,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1998), pp. 482–488.

Ma, S.

S. Ma, “Conics-based stereo, motion estimation, and pose determination,” Int. J. Comput. Vis. 10, 7–25 (1993).
[CrossRef]

Ma, Y.

Y. Ma, S. Soatto, J. Koseck, and S. S. Sastry, An Invitation to 3-D Vision (Springer, 2003).

Manjunath, B. S.

M. Zuliani, C. S. Kenney, and B. S. Manjunath, “The multiRANSAC algorithm and its application to detect planar homographies,” in Proceedings of the International Conference on Image Processing (IEEE, 2005), pp. III, 153–156.

Marinos, C.

C. Rothwell, A. Zisserman, C. Marinos, D. Forsyth, and J. Mundy, “Relative motion and pose from arbitrary plane curves,” Image Vis. Comput. 10, 250–262 (1992).
[CrossRef]

Maybank, S.

P. Sturm and S. Maybank, “On plane-based camera calibration: a general algorithm, singularities, applications,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 432–437.

Mundy, J.

C. Rothwell, A. Zisserman, C. Marinos, D. Forsyth, and J. Mundy, “Relative motion and pose from arbitrary plane curves,” Image Vis. Comput. 10, 250–262 (1992).
[CrossRef]

Payrissat, R.

P. Gurdjos, A. Crouzil, and R. Payrissat, “Another way of looking at plane-based calibration: the Centre Circle constraint,” in Proceedings of the European Conference on Computer Vision (Springer, 2002), pp. 252–266.

Poncelet, J. V.

J. V. Poncelet, Applications d’Analyse et de Geometrie—Traite des Proprietes Projectives des Figures, Tome I (Imprimerie de Mallet-Bachelier, 1862).

Rothwell, C.

C. Rothwell, A. Zisserman, C. Marinos, D. Forsyth, and J. Mundy, “Relative motion and pose from arbitrary plane curves,” Image Vis. Comput. 10, 250–262 (1992).
[CrossRef]

Sastry, S. S.

Y. Ma, S. Soatto, J. Koseck, and S. S. Sastry, An Invitation to 3-D Vision (Springer, 2003).

Soatto, S.

Y. Ma, S. Soatto, J. Koseck, and S. S. Sastry, An Invitation to 3-D Vision (Springer, 2003).

Sturm, P.

P. Sturm and S. Maybank, “On plane-based camera calibration: a general algorithm, singularities, applications,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 432–437.

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Patt. Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

Zisserman, A.

C. Rothwell, A. Zisserman, C. Marinos, D. Forsyth, and J. Mundy, “Relative motion and pose from arbitrary plane curves,” Image Vis. Comput. 10, 250–262 (1992).
[CrossRef]

D. Liebowitz and A. Zisserman, “Metric rectification for perspective images of planes,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1998), pp. 482–488.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University, 2003).

Zuliani, M.

M. Zuliani, C. S. Kenney, and B. S. Manjunath, “The multiRANSAC algorithm and its application to detect planar homographies,” in Proceedings of the International Conference on Image Processing (IEEE, 2005), pp. III, 153–156.

Commun. ACM

M. A. Fischler and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM 24, 381–395 (1981).
[CrossRef]

IEEE Trans. Patt. Anal. Mach. Intell.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Patt. Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

Image Vis. Comput.

C. Rothwell, A. Zisserman, C. Marinos, D. Forsyth, and J. Mundy, “Relative motion and pose from arbitrary plane curves,” Image Vis. Comput. 10, 250–262 (1992).
[CrossRef]

Int. J. Comput. Vis.

S. Ma, “Conics-based stereo, motion estimation, and pose determination,” Int. J. Comput. Vis. 10, 7–25 (1993).
[CrossRef]

Other

P. Sturm and S. Maybank, “On plane-based camera calibration: a general algorithm, singularities, applications,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 432–437.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University, 2003).

D. Liebowitz and A. Zisserman, “Metric rectification for perspective images of planes,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1998), pp. 482–488.

J. Bouguet, Camera Calibration Toolbox for MATLAB, http://www.vision.caltech.edu/bouguetj/calib_doc/ .

Y. Ma, S. Soatto, J. Koseck, and S. S. Sastry, An Invitation to 3-D Vision (Springer, 2003).

M. Zuliani, C. S. Kenney, and B. S. Manjunath, “The multiRANSAC algorithm and its application to detect planar homographies,” in Proceedings of the International Conference on Image Processing (IEEE, 2005), pp. III, 153–156.

https://github.com/RANSAC/RANSAC-Toolbox .

P. Gurdjos, A. Crouzil, and R. Payrissat, “Another way of looking at plane-based calibration: the Centre Circle constraint,” in Proceedings of the European Conference on Computer Vision (Springer, 2002), pp. 252–266.

J. V. Poncelet, Applications d’Analyse et de Geometrie—Traite des Proprietes Projectives des Figures, Tome I (Imprimerie de Mallet-Bachelier, 1862).

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Figures (11)

Fig. 1.
Fig. 1.

One quadrangle image.

Fig. 2.
Fig. 2.

Three coplanar batteries.

Fig. 3.
Fig. 3.

Two noncoplanar instruments.

Fig. 4.
Fig. 4.

Quadrangle ABCD and its diagonal triangle OXY.

Fig. 5.
Fig. 5.

Centrosymmetric quadrangles: (a) parallelogram (including the rectangle) and (b) square.

Fig. 6.
Fig. 6.

Center circle and the cuboid bound.

Fig. 7.
Fig. 7.

Flow diagram of removing the wrong correspondences for four coplanar points.

Fig. 8.
Fig. 8.

Simulated pattern consisting of three quadrangles.

Fig. 9.
Fig. 9.

Eight center lines passing through the square region of the principal point.

Fig. 10.
Fig. 10.

Rectified image.

Fig. 11.
Fig. 11.

Two reprojection results. × denotes one reprojected point. The two numbers under each rectangle denote its approximate size.

Tables (7)

Tables Icon

Table 1. Residual PoC with Respect to the Possibly Flipped Vertices

Tables Icon

Table 2. Automatic Detection of Coplanar Quadrangle Objects Using RANSAC Combined with the Cuboid Bound Constraint

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Table 3. Numbers of PoC Satisfying the Cuboid Bound Constraint in 10,000 Independent Experiments under Different Cuboid Parameters

Tables Icon

Table 4. Errors after Utilizing the Second Image

Tables Icon

Table 5. fu Results of Different Combinations of Three Imagesa

Tables Icon

Table 6. Calibration Results

Tables Icon

Table 7. PoC Satisfying the Cuboid Bound Constraint for Three Batteriesa

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

[ABCD][abcd][bcda][cdab][dabc].
H=K[r1,r2,t],withK=[fu0τfv01],
μm=HM,
h1TKTK1h2=0,
h1TKTK1h1=h2TKTK1h2,
H¯=[1n(H11H31+H12H32)1n(H12H31H11H32)H131n(H21H31+H22H32)1n(H22H31H21H32)H23n0H33],
η1(u˜u˜S)+η2(v˜v˜S)+η3(w˜w˜S)=0,
(u˜u˜S)2+(v˜v˜S)2+(w˜w˜S)2ρS2=0,
η=[H¯31H¯12,1τH¯31H¯22,0]T.
u˜S=H¯11H¯31,v˜S=1τH¯21H¯31,w˜S=0,ρS=H¯212+τ2H¯222|H¯31|.

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